Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.1% → 82.2%

Time: 19.9s

Alternatives: 16

Speedup: 1.9×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]

Initial Program: 56.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]

Alternative 1: 82.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{27464.7644705}{x \cdot x}\\ t_2 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ t_3 := \frac{z}{x \cdot x}\\ t_4 := \frac{a}{x} - t\_3\\ \mathbf{if}\;y \leq -6 \cdot 10^{+192}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+34}:\\ \;\;\;\;\frac{-1}{\frac{t\_3 + \left(\frac{\frac{\left(\frac{230661.510616}{x \cdot x} - \frac{c}{x}\right) + \left(z \cdot \frac{\frac{b}{x} + \left(z \cdot \frac{t\_3 - \frac{a}{x}}{x} - t\_1\right)}{x} + \frac{t\_4 \cdot 27464.7644705}{x}\right)}{y} + \left(\left(z \cdot \frac{t\_4}{x} + t\_1\right) - \frac{b}{x}\right)}{y} - \frac{a}{x}\right)}{y} + \frac{-1}{x}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+43}:\\ \;\;\;\;\frac{y \cdot \frac{-1}{\frac{-1}{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}} + t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+164}:\\ \;\;\;\;\frac{-1}{\frac{t\_3 + \left(\frac{\left(t\_1 + \frac{z \cdot t\_4}{x}\right) - \frac{b}{x}}{y} - \frac{a}{x}\right)}{y} + \frac{-1}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (/ 27464.7644705 (* x x)))
        (t_2 (- (+ x (/ z y)) (/ (* x a) y)))
        (t_3 (/ z (* x x)))
        (t_4 (- (/ a x) t_3)))
   (if (<= y -6e+192)
     t_2
     (if (<= y -9.2e+34)
       (/
        -1.0
        (+
         (/
          (+
           t_3
           (-
            (/
             (+
              (/
               (+
                (- (/ 230661.510616 (* x x)) (/ c x))
                (+
                 (* z (/ (+ (/ b x) (- (* z (/ (- t_3 (/ a x)) x)) t_1)) x))
                 (/ (* t_4 27464.7644705) x)))
               y)
              (- (+ (* z (/ t_4 x)) t_1) (/ b x)))
             y)
            (/ a x)))
          y)
         (/ -1.0 x)))
       (if (<= y 1.2e+43)
         (/
          (+
           (*
            y
            (/
             -1.0
             (/
              -1.0
              (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))))))
           t)
          (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))
         (if (<= y 6.5e+164)
           (/
            -1.0
            (+
             (/
              (+ t_3 (- (/ (- (+ t_1 (/ (* z t_4) x)) (/ b x)) y) (/ a x)))
              y)
             (/ -1.0 x)))
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 27464.7644705 / (x * x);
	double t_2 = (x + (z / y)) - ((x * a) / y);
	double t_3 = z / (x * x);
	double t_4 = (a / x) - t_3;
	double tmp;
	if (y <= -6e+192) {
		tmp = t_2;
	} else if (y <= -9.2e+34) {
		tmp = -1.0 / (((t_3 + (((((((230661.510616 / (x * x)) - (c / x)) + ((z * (((b / x) + ((z * ((t_3 - (a / x)) / x)) - t_1)) / x)) + ((t_4 * 27464.7644705) / x))) / y) + (((z * (t_4 / x)) + t_1) - (b / x))) / y) - (a / x))) / y) + (-1.0 / x));
	} else if (y <= 1.2e+43) {
		tmp = ((y * (-1.0 / (-1.0 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))))) + t) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else if (y <= 6.5e+164) {
		tmp = -1.0 / (((t_3 + ((((t_1 + ((z * t_4) / x)) - (b / x)) / y) - (a / x))) / y) + (-1.0 / x));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = 27464.7644705d0 / (x * x)
    t_2 = (x + (z / y)) - ((x * a) / y)
    t_3 = z / (x * x)
    t_4 = (a / x) - t_3
    if (y <= (-6d+192)) then
        tmp = t_2
    else if (y <= (-9.2d+34)) then
        tmp = (-1.0d0) / (((t_3 + (((((((230661.510616d0 / (x * x)) - (c / x)) + ((z * (((b / x) + ((z * ((t_3 - (a / x)) / x)) - t_1)) / x)) + ((t_4 * 27464.7644705d0) / x))) / y) + (((z * (t_4 / x)) + t_1) - (b / x))) / y) - (a / x))) / y) + ((-1.0d0) / x))
    else if (y <= 1.2d+43) then
        tmp = ((y * ((-1.0d0) / ((-1.0d0) / (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x))))))))) + t) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    else if (y <= 6.5d+164) then
        tmp = (-1.0d0) / (((t_3 + ((((t_1 + ((z * t_4) / x)) - (b / x)) / y) - (a / x))) / y) + ((-1.0d0) / x))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = 27464.7644705 / (x * x);
	double t_2 = (x + (z / y)) - ((x * a) / y);
	double t_3 = z / (x * x);
	double t_4 = (a / x) - t_3;
	double tmp;
	if (y <= -6e+192) {
		tmp = t_2;
	} else if (y <= -9.2e+34) {
		tmp = -1.0 / (((t_3 + (((((((230661.510616 / (x * x)) - (c / x)) + ((z * (((b / x) + ((z * ((t_3 - (a / x)) / x)) - t_1)) / x)) + ((t_4 * 27464.7644705) / x))) / y) + (((z * (t_4 / x)) + t_1) - (b / x))) / y) - (a / x))) / y) + (-1.0 / x));
	} else if (y <= 1.2e+43) {
		tmp = ((y * (-1.0 / (-1.0 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))))) + t) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else if (y <= 6.5e+164) {
		tmp = -1.0 / (((t_3 + ((((t_1 + ((z * t_4) / x)) - (b / x)) / y) - (a / x))) / y) + (-1.0 / x));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = 27464.7644705 / (x * x)
	t_2 = (x + (z / y)) - ((x * a) / y)
	t_3 = z / (x * x)
	t_4 = (a / x) - t_3
	tmp = 0
	if y <= -6e+192:
		tmp = t_2
	elif y <= -9.2e+34:
		tmp = -1.0 / (((t_3 + (((((((230661.510616 / (x * x)) - (c / x)) + ((z * (((b / x) + ((z * ((t_3 - (a / x)) / x)) - t_1)) / x)) + ((t_4 * 27464.7644705) / x))) / y) + (((z * (t_4 / x)) + t_1) - (b / x))) / y) - (a / x))) / y) + (-1.0 / x))
	elif y <= 1.2e+43:
		tmp = ((y * (-1.0 / (-1.0 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))))) + t) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	elif y <= 6.5e+164:
		tmp = -1.0 / (((t_3 + ((((t_1 + ((z * t_4) / x)) - (b / x)) / y) - (a / x))) / y) + (-1.0 / x))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(27464.7644705 / Float64(x * x))
	t_2 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	t_3 = Float64(z / Float64(x * x))
	t_4 = Float64(Float64(a / x) - t_3)
	tmp = 0.0
	if (y <= -6e+192)
		tmp = t_2;
	elseif (y <= -9.2e+34)
		tmp = Float64(-1.0 / Float64(Float64(Float64(t_3 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(230661.510616 / Float64(x * x)) - Float64(c / x)) + Float64(Float64(z * Float64(Float64(Float64(b / x) + Float64(Float64(z * Float64(Float64(t_3 - Float64(a / x)) / x)) - t_1)) / x)) + Float64(Float64(t_4 * 27464.7644705) / x))) / y) + Float64(Float64(Float64(z * Float64(t_4 / x)) + t_1) - Float64(b / x))) / y) - Float64(a / x))) / y) + Float64(-1.0 / x)));
	elseif (y <= 1.2e+43)
		tmp = Float64(Float64(Float64(y * Float64(-1.0 / Float64(-1.0 / Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))))) + t) / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	elseif (y <= 6.5e+164)
		tmp = Float64(-1.0 / Float64(Float64(Float64(t_3 + Float64(Float64(Float64(Float64(t_1 + Float64(Float64(z * t_4) / x)) - Float64(b / x)) / y) - Float64(a / x))) / y) + Float64(-1.0 / x)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = 27464.7644705 / (x * x);
	t_2 = (x + (z / y)) - ((x * a) / y);
	t_3 = z / (x * x);
	t_4 = (a / x) - t_3;
	tmp = 0.0;
	if (y <= -6e+192)
		tmp = t_2;
	elseif (y <= -9.2e+34)
		tmp = -1.0 / (((t_3 + (((((((230661.510616 / (x * x)) - (c / x)) + ((z * (((b / x) + ((z * ((t_3 - (a / x)) / x)) - t_1)) / x)) + ((t_4 * 27464.7644705) / x))) / y) + (((z * (t_4 / x)) + t_1) - (b / x))) / y) - (a / x))) / y) + (-1.0 / x));
	elseif (y <= 1.2e+43)
		tmp = ((y * (-1.0 / (-1.0 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))))) + t) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	elseif (y <= 6.5e+164)
		tmp = -1.0 / (((t_3 + ((((t_1 + ((z * t_4) / x)) - (b / x)) / y) - (a / x))) / y) + (-1.0 / x));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(27464.7644705 / N[(x * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(a / x), $MachinePrecision] - t$95$3), $MachinePrecision]}, If[LessEqual[y, -6e+192], t$95$2, If[LessEqual[y, -9.2e+34], N[(-1.0 / N[(N[(N[(t$95$3 + N[(N[(N[(N[(N[(N[(N[(230661.510616 / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(c / x), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(N[(b / x), $MachinePrecision] + N[(N[(z * N[(N[(t$95$3 - N[(a / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$4 * 27464.7644705), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(N[(N[(z * N[(t$95$4 / x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(b / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+43], N[(N[(N[(y * N[(-1.0 / N[(-1.0 / N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+164], N[(-1.0 / N[(N[(N[(t$95$3 + N[(N[(N[(N[(t$95$1 + N[(N[(z * t$95$4), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(b / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6e192 or 6.5000000000000003e164 < y

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)}{y}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)}{y}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), y\right)\right) \]

      9. *-lowering-*.f64 92.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   5. Simplified 92.4%

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]

   if -6e192 < y < -9.1999999999999993e34

   1. Initial program 7.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right)\right) \]

   4. Applied egg-rr 7.5%

      \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}}} \]
   5. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\left(\left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}\right) \cdot y\right), t\right)\right)\right) \]

      2. remove-double-div N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\left(\frac{1}{\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}}} \cdot y\right), t\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\left(\frac{1 \cdot y}{\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}}}\right), t\right)\right)\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\left(\frac{1}{\frac{\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}}}{1 \cdot y}}\right), t\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}}}{1 \cdot y}\right)\right), t\right)\right)\right) \]

      6. *-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}}}{y}\right)\right), t\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}}\right), y\right)\right), t\right)\right)\right) \]

   6. Applied egg-rr 7.5%

      \[\leadsto \frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{\color{blue}{\frac{1}{\frac{\frac{1}{y \cdot \left(y \cdot \left(z + y \cdot x\right) + 27464.7644705\right) + 230661.510616}}{y}}} + t}} \]

   7. Taylor expanded in y around -inf

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(-1 \cdot \frac{\left(-1 \cdot \frac{a}{x} + -1 \cdot \frac{\left(-1 \cdot \frac{\left(-1 \cdot \frac{c}{x} + \frac{28832688827}{125000} \cdot \frac{1}{{x}^{2}}\right) - \left(-1 \cdot \frac{z \cdot \left(\frac{b}{x} - \left(-1 \cdot \frac{z \cdot \left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right)}{x} + \frac{54929528941}{2000000} \cdot \frac{1}{{x}^{2}}\right)\right)}{x} + \frac{54929528941}{2000000} \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{x}\right)}{y} + \frac{b}{x}\right) - \left(-1 \cdot \frac{z \cdot \left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right)}{x} + \frac{54929528941}{2000000} \cdot \frac{1}{{x}^{2}}\right)}{y}\right) - -1 \cdot \frac{z}{{x}^{2}}}{y} + \frac{1}{x}\right)}\right) \]

   9. Simplified 76.5%

      \[\leadsto \frac{1}{\color{blue}{\left(-\frac{-1 \cdot \left(\frac{a}{x} + \frac{\left(-\frac{\left(\left(-\frac{c}{x}\right) + \frac{230661.510616}{x \cdot x}\right) - \left(\left(-z \cdot \frac{\frac{b}{x} - \left(\left(-z \cdot \frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{x}\right) + \frac{27464.7644705}{x \cdot x}\right)}{x}\right) + \frac{27464.7644705 \cdot \left(-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)\right)}{x}\right)}{y}\right) + \left(\frac{b}{x} - \left(\left(-z \cdot \frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{x}\right) + \frac{27464.7644705}{x \cdot x}\right)\right)}{y}\right) + 1 \cdot \frac{z}{x \cdot x}}{y}\right) + \frac{1}{x}}} \]

   if -9.1999999999999993e34 < y < 1.20000000000000012e43

   1. Initial program 94.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip-+ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right)}, c\right), y\right), i\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right)}, c\right), y\right), i\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right)}, c\right), y\right), i\right)\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}}\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), \color{blue}{y}\right), c\right), y\right), i\right)\right) \]

      5. flip-+ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}}\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), \color{blue}{y}\right), c\right), y\right), i\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right), \frac{28832688827}{125000}\right)\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   4. Applied egg-rr 94.8%

      \[\leadsto \frac{\color{blue}{\frac{1}{\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616}}} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 1.20000000000000012e43 < y < 6.5000000000000003e164

   1. Initial program 3.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right)\right) \]

   4. Applied egg-rr 3.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}}} \]

   5. Taylor expanded in y around -inf

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(-1 \cdot \frac{\left(-1 \cdot \frac{a}{x} + -1 \cdot \frac{\frac{b}{x} - \left(-1 \cdot \frac{z \cdot \left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right)}{x} + \frac{54929528941}{2000000} \cdot \frac{1}{{x}^{2}}\right)}{y}\right) - -1 \cdot \frac{z}{{x}^{2}}}{y} + \frac{1}{x}\right)}\right) \]

   7. Simplified 68.6%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + \left(-\frac{-1 \cdot \left(\frac{a}{x} + \frac{\frac{b}{x} - \left(\frac{27464.7644705}{x \cdot x} + \left(-\frac{z \cdot \left(-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)\right)}{x}\right)\right)}{y}\right) + 1 \cdot \frac{z}{x \cdot x}}{y}\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+192}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+34}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} + \left(\frac{\frac{\left(\frac{230661.510616}{x \cdot x} - \frac{c}{x}\right) + \left(z \cdot \frac{\frac{b}{x} + \left(z \cdot \frac{\frac{z}{x \cdot x} - \frac{a}{x}}{x} - \frac{27464.7644705}{x \cdot x}\right)}{x} + \frac{\left(\frac{a}{x} - \frac{z}{x \cdot x}\right) \cdot 27464.7644705}{x}\right)}{y} + \left(\left(z \cdot \frac{\frac{a}{x} - \frac{z}{x \cdot x}}{x} + \frac{27464.7644705}{x \cdot x}\right) - \frac{b}{x}\right)}{y} - \frac{a}{x}\right)}{y} + \frac{-1}{x}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+43}:\\ \;\;\;\;\frac{y \cdot \frac{-1}{\frac{-1}{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}} + t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+164}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} + \left(\frac{\left(\frac{27464.7644705}{x \cdot x} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{x}\right) - \frac{b}{x}}{y} - \frac{a}{x}\right)}{y} + \frac{-1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ t_2 := \frac{z}{x \cdot x}\\ t_3 := \frac{-1}{\frac{t\_2 + \left(\frac{\left(\frac{27464.7644705}{x \cdot x} + \frac{z \cdot \left(\frac{a}{x} - t\_2\right)}{x}\right) - \frac{b}{x}}{y} - \frac{a}{x}\right)}{y} + \frac{-1}{x}}\\ \mathbf{if}\;y \leq -6 \cdot 10^{+192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{+53}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+42}:\\ \;\;\;\;\frac{y \cdot \frac{-1}{\frac{-1}{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}} + t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+166}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y)))
        (t_2 (/ z (* x x)))
        (t_3
         (/
          -1.0
          (+
           (/
            (+
             t_2
             (-
              (/
               (-
                (+ (/ 27464.7644705 (* x x)) (/ (* z (- (/ a x) t_2)) x))
                (/ b x))
               y)
              (/ a x)))
            y)
           (/ -1.0 x)))))
   (if (<= y -6e+192)
     t_1
     (if (<= y -1.22e+53)
       t_3
       (if (<= y 4.4e+42)
         (/
          (+
           (*
            y
            (/
             -1.0
             (/
              -1.0
              (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))))))
           t)
          (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))
         (if (<= y 4.2e+166) t_3 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double t_2 = z / (x * x);
	double t_3 = -1.0 / (((t_2 + (((((27464.7644705 / (x * x)) + ((z * ((a / x) - t_2)) / x)) - (b / x)) / y) - (a / x))) / y) + (-1.0 / x));
	double tmp;
	if (y <= -6e+192) {
		tmp = t_1;
	} else if (y <= -1.22e+53) {
		tmp = t_3;
	} else if (y <= 4.4e+42) {
		tmp = ((y * (-1.0 / (-1.0 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))))) + t) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else if (y <= 4.2e+166) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x + (z / y)) - ((x * a) / y)
    t_2 = z / (x * x)
    t_3 = (-1.0d0) / (((t_2 + (((((27464.7644705d0 / (x * x)) + ((z * ((a / x) - t_2)) / x)) - (b / x)) / y) - (a / x))) / y) + ((-1.0d0) / x))
    if (y <= (-6d+192)) then
        tmp = t_1
    else if (y <= (-1.22d+53)) then
        tmp = t_3
    else if (y <= 4.4d+42) then
        tmp = ((y * ((-1.0d0) / ((-1.0d0) / (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x))))))))) + t) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    else if (y <= 4.2d+166) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double t_2 = z / (x * x);
	double t_3 = -1.0 / (((t_2 + (((((27464.7644705 / (x * x)) + ((z * ((a / x) - t_2)) / x)) - (b / x)) / y) - (a / x))) / y) + (-1.0 / x));
	double tmp;
	if (y <= -6e+192) {
		tmp = t_1;
	} else if (y <= -1.22e+53) {
		tmp = t_3;
	} else if (y <= 4.4e+42) {
		tmp = ((y * (-1.0 / (-1.0 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))))) + t) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else if (y <= 4.2e+166) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	t_2 = z / (x * x)
	t_3 = -1.0 / (((t_2 + (((((27464.7644705 / (x * x)) + ((z * ((a / x) - t_2)) / x)) - (b / x)) / y) - (a / x))) / y) + (-1.0 / x))
	tmp = 0
	if y <= -6e+192:
		tmp = t_1
	elif y <= -1.22e+53:
		tmp = t_3
	elif y <= 4.4e+42:
		tmp = ((y * (-1.0 / (-1.0 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))))) + t) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	elif y <= 4.2e+166:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	t_2 = Float64(z / Float64(x * x))
	t_3 = Float64(-1.0 / Float64(Float64(Float64(t_2 + Float64(Float64(Float64(Float64(Float64(27464.7644705 / Float64(x * x)) + Float64(Float64(z * Float64(Float64(a / x) - t_2)) / x)) - Float64(b / x)) / y) - Float64(a / x))) / y) + Float64(-1.0 / x)))
	tmp = 0.0
	if (y <= -6e+192)
		tmp = t_1;
	elseif (y <= -1.22e+53)
		tmp = t_3;
	elseif (y <= 4.4e+42)
		tmp = Float64(Float64(Float64(y * Float64(-1.0 / Float64(-1.0 / Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))))) + t) / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	elseif (y <= 4.2e+166)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	t_2 = z / (x * x);
	t_3 = -1.0 / (((t_2 + (((((27464.7644705 / (x * x)) + ((z * ((a / x) - t_2)) / x)) - (b / x)) / y) - (a / x))) / y) + (-1.0 / x));
	tmp = 0.0;
	if (y <= -6e+192)
		tmp = t_1;
	elseif (y <= -1.22e+53)
		tmp = t_3;
	elseif (y <= 4.4e+42)
		tmp = ((y * (-1.0 / (-1.0 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))))) + t) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	elseif (y <= 4.2e+166)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-1.0 / N[(N[(N[(t$95$2 + N[(N[(N[(N[(N[(27464.7644705 / N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(a / x), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(b / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+192], t$95$1, If[LessEqual[y, -1.22e+53], t$95$3, If[LessEqual[y, 4.4e+42], N[(N[(N[(y * N[(-1.0 / N[(-1.0 / N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+166], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6e192 or 4.2000000000000001e166 < y

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)}{y}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)}{y}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), y\right)\right) \]

      9. *-lowering-*.f64 92.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   5. Simplified 92.4%

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]

   if -6e192 < y < -1.21999999999999999e53 or 4.4000000000000003e42 < y < 4.2000000000000001e166

   1. Initial program 4.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right)\right) \]

   4. Applied egg-rr 4.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}}} \]

   5. Taylor expanded in y around -inf

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(-1 \cdot \frac{\left(-1 \cdot \frac{a}{x} + -1 \cdot \frac{\frac{b}{x} - \left(-1 \cdot \frac{z \cdot \left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right)}{x} + \frac{54929528941}{2000000} \cdot \frac{1}{{x}^{2}}\right)}{y}\right) - -1 \cdot \frac{z}{{x}^{2}}}{y} + \frac{1}{x}\right)}\right) \]

   7. Simplified 71.0%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + \left(-\frac{-1 \cdot \left(\frac{a}{x} + \frac{\frac{b}{x} - \left(\frac{27464.7644705}{x \cdot x} + \left(-\frac{z \cdot \left(-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)\right)}{x}\right)\right)}{y}\right) + 1 \cdot \frac{z}{x \cdot x}}{y}\right)}} \]

   if -1.21999999999999999e53 < y < 4.4000000000000003e42

   1. Initial program 94.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip-+ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right)}, c\right), y\right), i\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right)}, c\right), y\right), i\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right)}, c\right), y\right), i\right)\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}}\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), \color{blue}{y}\right), c\right), y\right), i\right)\right) \]

      5. flip-+ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}}\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), \color{blue}{y}\right), c\right), y\right), i\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right), \frac{28832688827}{125000}\right)\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   4. Applied egg-rr 94.2%

      \[\leadsto \frac{\color{blue}{\frac{1}{\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616}}} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+192}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{+53}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} + \left(\frac{\left(\frac{27464.7644705}{x \cdot x} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{x}\right) - \frac{b}{x}}{y} - \frac{a}{x}\right)}{y} + \frac{-1}{x}}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+42}:\\ \;\;\;\;\frac{y \cdot \frac{-1}{\frac{-1}{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}} + t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+166}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} + \left(\frac{\left(\frac{27464.7644705}{x \cdot x} + \frac{z \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{x}\right) - \frac{b}{x}}{y} - \frac{a}{x}\right)}{y} + \frac{-1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -5.1 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+41}:\\ \;\;\;\;\frac{y \cdot \frac{-1}{\frac{-1}{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}} + t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+166}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -5.1e+61)
     t_1
     (if (<= y 9e+41)
       (/
        (+
         (*
          y
          (/
           -1.0
           (/
            -1.0
            (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x)))))))))
         t)
        (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))
       (if (<= y 1.2e+166)
         (/ -1.0 (+ (/ (- (/ z (* x x)) (/ a x)) y) (/ -1.0 x)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -5.1e+61) {
		tmp = t_1;
	} else if (y <= 9e+41) {
		tmp = ((y * (-1.0 / (-1.0 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))))) + t) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else if (y <= 1.2e+166) {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-5.1d+61)) then
        tmp = t_1
    else if (y <= 9d+41) then
        tmp = ((y * ((-1.0d0) / ((-1.0d0) / (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x))))))))) + t) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    else if (y <= 1.2d+166) then
        tmp = (-1.0d0) / ((((z / (x * x)) - (a / x)) / y) + ((-1.0d0) / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -5.1e+61) {
		tmp = t_1;
	} else if (y <= 9e+41) {
		tmp = ((y * (-1.0 / (-1.0 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))))) + t) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else if (y <= 1.2e+166) {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -5.1e+61:
		tmp = t_1
	elif y <= 9e+41:
		tmp = ((y * (-1.0 / (-1.0 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))))) + t) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	elif y <= 1.2e+166:
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -5.1e+61)
		tmp = t_1;
	elseif (y <= 9e+41)
		tmp = Float64(Float64(Float64(y * Float64(-1.0 / Float64(-1.0 / Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x))))))))) + t) / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	elseif (y <= 1.2e+166)
		tmp = Float64(-1.0 / Float64(Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y) + Float64(-1.0 / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -5.1e+61)
		tmp = t_1;
	elseif (y <= 9e+41)
		tmp = ((y * (-1.0 / (-1.0 / (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x))))))))) + t) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	elseif (y <= 1.2e+166)
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.1e+61], t$95$1, If[LessEqual[y, 9e+41], N[(N[(N[(y * N[(-1.0 / N[(-1.0 / N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+166], N[(-1.0 / N[(N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.1000000000000001e61 or 1.19999999999999996e166 < y

   1. Initial program 1.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)}{y}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)}{y}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), y\right)\right) \]

      9. *-lowering-*.f64 78.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   5. Simplified 78.2%

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]

   if -5.1000000000000001e61 < y < 9.0000000000000002e41

   1. Initial program 94.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip-+ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right)}, c\right), y\right), i\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right)}, c\right), y\right), i\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right)}, c\right), y\right), i\right)\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) \cdot \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right) - \frac{28832688827}{125000} \cdot \frac{28832688827}{125000}}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y - \frac{28832688827}{125000}}}\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), \color{blue}{y}\right), c\right), y\right), i\right)\right) \]

      5. flip-+ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}}\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), \color{blue}{y}\right), c\right), y\right), i\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y\right), \frac{28832688827}{125000}\right)\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]

   4. Applied egg-rr 94.2%

      \[\leadsto \frac{\color{blue}{\frac{1}{\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616}}} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 9.0000000000000002e41 < y < 1.19999999999999996e166

   1. Initial program 3.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right)\right) \]

   4. Applied egg-rr 3.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}}} \]

   5. Taylor expanded in y around -inf

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y} + \frac{1}{x}\right)}\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{x} + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(\frac{1}{x}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \left(\color{blue}{-1} \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right), y\right)\right)\right)\right) \]

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{a}{x}\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right)\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left({x}^{2}\right)\right)\right)\right), y\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left(x \cdot x\right)\right)\right)\right), y\right)\right)\right)\right) \]

      13. *-lowering-*.f64 67.5%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right)\right)\right)\right) \]

   7. Simplified 67.5%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + \left(-\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{y}\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+61}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+41}:\\ \;\;\;\;\frac{y \cdot \frac{-1}{\frac{-1}{230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)}} + t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+166}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+43}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+166}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -3.6e+52)
     t_1
     (if (<= y 3.2e+43)
       (/
        (+
         t
         (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
        (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))
       (if (<= y 9.2e+166)
         (/ -1.0 (+ (/ (- (/ z (* x x)) (/ a x)) y) (/ -1.0 x)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -3.6e+52) {
		tmp = t_1;
	} else if (y <= 3.2e+43) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else if (y <= 9.2e+166) {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-3.6d+52)) then
        tmp = t_1
    else if (y <= 3.2d+43) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    else if (y <= 9.2d+166) then
        tmp = (-1.0d0) / ((((z / (x * x)) - (a / x)) / y) + ((-1.0d0) / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -3.6e+52) {
		tmp = t_1;
	} else if (y <= 3.2e+43) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else if (y <= 9.2e+166) {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -3.6e+52:
		tmp = t_1
	elif y <= 3.2e+43:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	elif y <= 9.2e+166:
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -3.6e+52)
		tmp = t_1;
	elseif (y <= 3.2e+43)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	elseif (y <= 9.2e+166)
		tmp = Float64(-1.0 / Float64(Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y) + Float64(-1.0 / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -3.6e+52)
		tmp = t_1;
	elseif (y <= 3.2e+43)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	elseif (y <= 9.2e+166)
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+52], t$95$1, If[LessEqual[y, 3.2e+43], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e+166], N[(-1.0 / N[(N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6e52 or 9.2000000000000003e166 < y

   1. Initial program 1.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)}{y}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)}{y}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), y\right)\right) \]

      9. *-lowering-*.f64 78.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   5. Simplified 78.2%

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]

   if -3.6e52 < y < 3.20000000000000014e43

   1. Initial program 94.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   if 3.20000000000000014e43 < y < 9.2000000000000003e166

   1. Initial program 3.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right)\right) \]

   4. Applied egg-rr 3.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}}} \]

   5. Taylor expanded in y around -inf

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y} + \frac{1}{x}\right)}\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{x} + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(\frac{1}{x}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \left(\color{blue}{-1} \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right), y\right)\right)\right)\right) \]

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{a}{x}\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right)\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left({x}^{2}\right)\right)\right)\right), y\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left(x \cdot x\right)\right)\right)\right), y\right)\right)\right)\right) \]

      13. *-lowering-*.f64 67.5%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right)\right)\right)\right) \]

   7. Simplified 67.5%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + \left(-\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{y}\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+52}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+43}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+166}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -7.6 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+37}:\\ \;\;\;\;\frac{-1}{\frac{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}{\frac{-1}{\frac{\frac{1}{230661.510616 + z \cdot \left(y \cdot y\right)}}{y}} - t}}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+165}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -7.6e+33)
     t_1
     (if (<= y 3e+37)
       (/
        -1.0
        (/
         (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i)
         (- (/ -1.0 (/ (/ 1.0 (+ 230661.510616 (* z (* y y)))) y)) t)))
       (if (<= y 6.6e+165)
         (/ -1.0 (+ (/ (- (/ z (* x x)) (/ a x)) y) (/ -1.0 x)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -7.6e+33) {
		tmp = t_1;
	} else if (y <= 3e+37) {
		tmp = -1.0 / (((y * (c + (y * (b + (y * (y + a)))))) + i) / ((-1.0 / ((1.0 / (230661.510616 + (z * (y * y)))) / y)) - t));
	} else if (y <= 6.6e+165) {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-7.6d+33)) then
        tmp = t_1
    else if (y <= 3d+37) then
        tmp = (-1.0d0) / (((y * (c + (y * (b + (y * (y + a)))))) + i) / (((-1.0d0) / ((1.0d0 / (230661.510616d0 + (z * (y * y)))) / y)) - t))
    else if (y <= 6.6d+165) then
        tmp = (-1.0d0) / ((((z / (x * x)) - (a / x)) / y) + ((-1.0d0) / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -7.6e+33) {
		tmp = t_1;
	} else if (y <= 3e+37) {
		tmp = -1.0 / (((y * (c + (y * (b + (y * (y + a)))))) + i) / ((-1.0 / ((1.0 / (230661.510616 + (z * (y * y)))) / y)) - t));
	} else if (y <= 6.6e+165) {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -7.6e+33:
		tmp = t_1
	elif y <= 3e+37:
		tmp = -1.0 / (((y * (c + (y * (b + (y * (y + a)))))) + i) / ((-1.0 / ((1.0 / (230661.510616 + (z * (y * y)))) / y)) - t))
	elif y <= 6.6e+165:
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -7.6e+33)
		tmp = t_1;
	elseif (y <= 3e+37)
		tmp = Float64(-1.0 / Float64(Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i) / Float64(Float64(-1.0 / Float64(Float64(1.0 / Float64(230661.510616 + Float64(z * Float64(y * y)))) / y)) - t)));
	elseif (y <= 6.6e+165)
		tmp = Float64(-1.0 / Float64(Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y) + Float64(-1.0 / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -7.6e+33)
		tmp = t_1;
	elseif (y <= 3e+37)
		tmp = -1.0 / (((y * (c + (y * (b + (y * (y + a)))))) + i) / ((-1.0 / ((1.0 / (230661.510616 + (z * (y * y)))) / y)) - t));
	elseif (y <= 6.6e+165)
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.6e+33], t$95$1, If[LessEqual[y, 3e+37], N[(-1.0 / N[(N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision] / N[(N[(-1.0 / N[(N[(1.0 / N[(230661.510616 + N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e+165], N[(-1.0 / N[(N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.60000000000000005e33 or 6.5999999999999997e165 < y

   1. Initial program 5.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)}{y}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)}{y}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), y\right)\right) \]

      9. *-lowering-*.f64 78.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   5. Simplified 78.1%

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]

   if -7.60000000000000005e33 < y < 3.00000000000000022e37

   1. Initial program 95.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right)\right) \]

   4. Applied egg-rr 95.2%

      \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}}} \]
   5. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\left(\left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}\right) \cdot y\right), t\right)\right)\right) \]

      2. remove-double-div N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\left(\frac{1}{\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}}} \cdot y\right), t\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\left(\frac{1 \cdot y}{\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}}}\right), t\right)\right)\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\left(\frac{1}{\frac{\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}}}{1 \cdot y}}\right), t\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}}}{1 \cdot y}\right)\right), t\right)\right)\right) \]

      6. *-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}}}{y}\right)\right), t\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}}\right), y\right)\right), t\right)\right)\right) \]

   6. Applied egg-rr 95.2%

      \[\leadsto \frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{\color{blue}{\frac{1}{\frac{\frac{1}{y \cdot \left(y \cdot \left(z + y \cdot x\right) + 27464.7644705\right) + 230661.510616}}{y}}} + t}} \]

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\color{blue}{\left({y}^{2} \cdot z\right)}, \frac{28832688827}{125000}\right)\right), y\right)\right), t\right)\right)\right) \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left({y}^{2}\right), z\right), \frac{28832688827}{125000}\right)\right), y\right)\right), t\right)\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(y \cdot y\right), z\right), \frac{28832688827}{125000}\right)\right), y\right)\right), t\right)\right)\right) \]

      3. *-lowering-*.f64 89.0%

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), z\right), \frac{28832688827}{125000}\right)\right), y\right)\right), t\right)\right)\right) \]

   9. Simplified 89.0%

      \[\leadsto \frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{\frac{1}{\frac{\frac{1}{\color{blue}{\left(y \cdot y\right) \cdot z} + 230661.510616}}{y}} + t}} \]

   if 3.00000000000000022e37 < y < 6.5999999999999997e165

   1. Initial program 6.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right)\right) \]

   4. Applied egg-rr 6.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}}} \]

   5. Taylor expanded in y around -inf

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y} + \frac{1}{x}\right)}\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{x} + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(\frac{1}{x}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \left(\color{blue}{-1} \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right), y\right)\right)\right)\right) \]

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{a}{x}\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right)\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left({x}^{2}\right)\right)\right)\right), y\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left(x \cdot x\right)\right)\right)\right), y\right)\right)\right)\right) \]

      13. *-lowering-*.f64 64.4%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right)\right)\right)\right) \]

   7. Simplified 64.4%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + \left(-\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{y}\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+33}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+37}:\\ \;\;\;\;\frac{-1}{\frac{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}{\frac{-1}{\frac{\frac{1}{230661.510616 + z \cdot \left(y \cdot y\right)}}{y}} - t}}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+165}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ t_2 := c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-34}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot t\_2 + i}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{t + z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{y}}{t\_2}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+164}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y)))
        (t_2 (+ c (* y (+ b (* y (+ y a)))))))
   (if (<= y -6.8e+30)
     t_1
     (if (<= y 1.1e-34)
       (/ (+ t (* y 230661.510616)) (+ (* y t_2) i))
       (if (<= y 4.2e+37)
         (/ (/ (+ t (* z (* y (* y y)))) y) t_2)
         (if (<= y 7e+164)
           (/ -1.0 (+ (/ (- (/ z (* x x)) (/ a x)) y) (/ -1.0 x)))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double t_2 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -6.8e+30) {
		tmp = t_1;
	} else if (y <= 1.1e-34) {
		tmp = (t + (y * 230661.510616)) / ((y * t_2) + i);
	} else if (y <= 4.2e+37) {
		tmp = ((t + (z * (y * (y * y)))) / y) / t_2;
	} else if (y <= 7e+164) {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + (z / y)) - ((x * a) / y)
    t_2 = c + (y * (b + (y * (y + a))))
    if (y <= (-6.8d+30)) then
        tmp = t_1
    else if (y <= 1.1d-34) then
        tmp = (t + (y * 230661.510616d0)) / ((y * t_2) + i)
    else if (y <= 4.2d+37) then
        tmp = ((t + (z * (y * (y * y)))) / y) / t_2
    else if (y <= 7d+164) then
        tmp = (-1.0d0) / ((((z / (x * x)) - (a / x)) / y) + ((-1.0d0) / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double t_2 = c + (y * (b + (y * (y + a))));
	double tmp;
	if (y <= -6.8e+30) {
		tmp = t_1;
	} else if (y <= 1.1e-34) {
		tmp = (t + (y * 230661.510616)) / ((y * t_2) + i);
	} else if (y <= 4.2e+37) {
		tmp = ((t + (z * (y * (y * y)))) / y) / t_2;
	} else if (y <= 7e+164) {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	t_2 = c + (y * (b + (y * (y + a))))
	tmp = 0
	if y <= -6.8e+30:
		tmp = t_1
	elif y <= 1.1e-34:
		tmp = (t + (y * 230661.510616)) / ((y * t_2) + i)
	elif y <= 4.2e+37:
		tmp = ((t + (z * (y * (y * y)))) / y) / t_2
	elif y <= 7e+164:
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	t_2 = Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))
	tmp = 0.0
	if (y <= -6.8e+30)
		tmp = t_1;
	elseif (y <= 1.1e-34)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * t_2) + i));
	elseif (y <= 4.2e+37)
		tmp = Float64(Float64(Float64(t + Float64(z * Float64(y * Float64(y * y)))) / y) / t_2);
	elseif (y <= 7e+164)
		tmp = Float64(-1.0 / Float64(Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y) + Float64(-1.0 / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	t_2 = c + (y * (b + (y * (y + a))));
	tmp = 0.0;
	if (y <= -6.8e+30)
		tmp = t_1;
	elseif (y <= 1.1e-34)
		tmp = (t + (y * 230661.510616)) / ((y * t_2) + i);
	elseif (y <= 4.2e+37)
		tmp = ((t + (z * (y * (y * y)))) / y) / t_2;
	elseif (y <= 7e+164)
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.8e+30], t$95$1, If[LessEqual[y, 1.1e-34], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * t$95$2), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+37], N[(N[(N[(t + N[(z * N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[y, 7e+164], N[(-1.0 / N[(N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.8000000000000005e30 or 6.9999999999999995e164 < y

   1. Initial program 5.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)}{y}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)}{y}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), y\right)\right) \]

      9. *-lowering-*.f64 78.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   5. Simplified 78.1%

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]

   if -6.8000000000000005e30 < y < 1.0999999999999999e-34

   1. Initial program 97.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{28832688827}{125000} \cdot y\right)}, t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right)}, y\right), i\right)\right) \]

      2. *-lowering-*.f64 89.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right)}, y\right), i\right)\right) \]

   5. Simplified 89.4%

      \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 1.0999999999999999e-34 < y < 4.2000000000000002e37

   1. Initial program 74.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\left({y}^{2} \cdot z\right)}, y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(z \cdot {y}^{2}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right)}, c\right), y\right), i\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \left({y}^{2}\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right)}, c\right), y\right), i\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \left(y \cdot y\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), \color{blue}{y}\right), c\right), y\right), i\right)\right) \]

      4. *-lowering-*.f64 42.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, y\right)\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), \color{blue}{y}\right), c\right), y\right), i\right)\right) \]

   5. Simplified 42.4%

      \[\leadsto \frac{\color{blue}{\left(z \cdot \left(y \cdot y\right)\right)} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in i around 0

      \[\leadsto \color{blue}{\frac{t + {y}^{3} \cdot z}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]
   7. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{\frac{t + {y}^{3} \cdot z}{y}}{\color{blue}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{t + {y}^{3} \cdot z}{y}\right), \color{blue}{\left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(t + {y}^{3} \cdot z\right), y\right), \left(\color{blue}{c} + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \left({y}^{3} \cdot z\right)\right), y\right), \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\left({y}^{3}\right), z\right)\right), y\right), \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      6. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\left(y \cdot \left(y \cdot y\right)\right), z\right)\right), y\right), \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\left(y \cdot {y}^{2}\right), z\right)\right), y\right), \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left({y}^{2}\right)\right), z\right)\right), y\right), \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      9. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \left(y \cdot y\right)\right), z\right)\right), y\right), \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      10. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right), z\right)\right), y\right), \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right), z\right)\right), y\right), \mathsf{+.f64}\left(c, \color{blue}{\left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right), z\right)\right), y\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \color{blue}{\left(b + y \cdot \left(a + y\right)\right)}\right)\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right), z\right)\right), y\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \color{blue}{\left(y \cdot \left(a + y\right)\right)}\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right), z\right)\right), y\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \color{blue}{\left(a + y\right)}\right)\right)\right)\right)\right) \]

      15. +-lowering-+.f64 54.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right), z\right)\right), y\right), \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \color{blue}{y}\right)\right)\right)\right)\right)\right) \]

   8. Simplified 54.7%

      \[\leadsto \color{blue}{\frac{\frac{t + \left(y \cdot \left(y \cdot y\right)\right) \cdot z}{y}}{c + y \cdot \left(b + y \cdot \left(a + y\right)\right)}} \]

   if 4.2000000000000002e37 < y < 6.9999999999999995e164

   1. Initial program 6.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right)\right) \]

   4. Applied egg-rr 6.3%

      \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}}} \]

   5. Taylor expanded in y around -inf

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y} + \frac{1}{x}\right)}\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{x} + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(\frac{1}{x}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \left(\color{blue}{-1} \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right), y\right)\right)\right)\right) \]

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{a}{x}\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right)\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left({x}^{2}\right)\right)\right)\right), y\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left(x \cdot x\right)\right)\right)\right), y\right)\right)\right)\right) \]

      13. *-lowering-*.f64 65.8%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right)\right)\right)\right) \]

   7. Simplified 65.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + \left(-\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{y}\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+30}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-34}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{t + z \cdot \left(y \cdot \left(y \cdot y\right)\right)}{y}}{c + y \cdot \left(b + y \cdot \left(y + a\right)\right)}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+164}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+40}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+165}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -7.2e+33)
     t_1
     (if (<= y 8e+40)
       (/
        (+
         t
         (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y (+ z (* y x))))))))
        (+ i (* y (+ c (* y b)))))
       (if (<= y 1.06e+165)
         (/ -1.0 (+ (/ (- (/ z (* x x)) (/ a x)) y) (/ -1.0 x)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -7.2e+33) {
		tmp = t_1;
	} else if (y <= 8e+40) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))));
	} else if (y <= 1.06e+165) {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-7.2d+33)) then
        tmp = t_1
    else if (y <= 8d+40) then
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))))
    else if (y <= 1.06d+165) then
        tmp = (-1.0d0) / ((((z / (x * x)) - (a / x)) / y) + ((-1.0d0) / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -7.2e+33) {
		tmp = t_1;
	} else if (y <= 8e+40) {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))));
	} else if (y <= 1.06e+165) {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -7.2e+33:
		tmp = t_1
	elif y <= 8e+40:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))))
	elif y <= 1.06e+165:
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -7.2e+33)
		tmp = t_1;
	elseif (y <= 8e+40)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * Float64(z + Float64(y * x)))))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	elseif (y <= 1.06e+165)
		tmp = Float64(-1.0 / Float64(Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y) + Float64(-1.0 / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -7.2e+33)
		tmp = t_1;
	elseif (y <= 8e+40)
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * (z + (y * x)))))))) / (i + (y * (c + (y * b))));
	elseif (y <= 1.06e+165)
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e+33], t$95$1, If[LessEqual[y, 8e+40], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.06e+165], N[(-1.0 / N[(N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.2000000000000005e33 or 1.0600000000000001e165 < y

   1. Initial program 5.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)}{y}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)}{y}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), y\right)\right) \]

      9. *-lowering-*.f64 78.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   5. Simplified 78.1%

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]

   if -7.2000000000000005e33 < y < 8.00000000000000024e40

   1. Initial program 94.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\color{blue}{\left(y \cdot \left(c + b \cdot y\right)\right)}, i\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(c + b \cdot y\right)\right), i\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \left(b \cdot y\right)\right)\right), i\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \left(y \cdot b\right)\right)\right), i\right)\right) \]

      4. *-lowering-*.f64 87.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right), y\right), \frac{54929528941}{2000000}\right), y\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(c, \mathsf{*.f64}\left(y, b\right)\right)\right), i\right)\right) \]

   5. Simplified 87.6%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{y \cdot \left(c + y \cdot b\right)} + i} \]

   if 8.00000000000000024e40 < y < 1.0600000000000001e165

   1. Initial program 3.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right)\right) \]

   4. Applied egg-rr 3.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}}} \]

   5. Taylor expanded in y around -inf

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y} + \frac{1}{x}\right)}\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{x} + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(\frac{1}{x}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \left(\color{blue}{-1} \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right), y\right)\right)\right)\right) \]

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{a}{x}\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right)\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left({x}^{2}\right)\right)\right)\right), y\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left(x \cdot x\right)\right)\right)\right), y\right)\right)\right)\right) \]

      13. *-lowering-*.f64 67.5%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right)\right)\right)\right) \]

   7. Simplified 67.5%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + \left(-\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{y}\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+33}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+40}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot \left(z + y \cdot x\right)\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+165}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+40}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+166}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -8.5e+32)
     t_1
     (if (<= y 7.8e+40)
       (/
        (+ t (* y (+ 230661.510616 (* y 27464.7644705))))
        (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))
       (if (<= y 4.8e+166)
         (/ -1.0 (+ (/ (- (/ z (* x x)) (/ a x)) y) (/ -1.0 x)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -8.5e+32) {
		tmp = t_1;
	} else if (y <= 7.8e+40) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else if (y <= 4.8e+166) {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-8.5d+32)) then
        tmp = t_1
    else if (y <= 7.8d+40) then
        tmp = (t + (y * (230661.510616d0 + (y * 27464.7644705d0)))) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    else if (y <= 4.8d+166) then
        tmp = (-1.0d0) / ((((z / (x * x)) - (a / x)) / y) + ((-1.0d0) / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -8.5e+32) {
		tmp = t_1;
	} else if (y <= 7.8e+40) {
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else if (y <= 4.8e+166) {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -8.5e+32:
		tmp = t_1
	elif y <= 7.8e+40:
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	elif y <= 4.8e+166:
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -8.5e+32)
		tmp = t_1;
	elseif (y <= 7.8e+40)
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * 27464.7644705)))) / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	elseif (y <= 4.8e+166)
		tmp = Float64(-1.0 / Float64(Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y) + Float64(-1.0 / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -8.5e+32)
		tmp = t_1;
	elseif (y <= 7.8e+40)
		tmp = (t + (y * (230661.510616 + (y * 27464.7644705)))) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	elseif (y <= 4.8e+166)
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+32], t$95$1, If[LessEqual[y, 7.8e+40], N[(N[(t + N[(y * N[(230661.510616 + N[(y * 27464.7644705), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+166], N[(-1.0 / N[(N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.4999999999999998e32 or 4.79999999999999984e166 < y

   1. Initial program 5.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)}{y}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)}{y}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), y\right)\right) \]

      9. *-lowering-*.f64 78.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   5. Simplified 78.1%

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]

   if -8.4999999999999998e32 < y < 7.8000000000000002e40

   1. Initial program 94.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{54929528941}{2000000} \cdot y\right)}, \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right)}, y\right), c\right), y\right), i\right)\right) \]

      2. *-lowering-*.f64 82.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{54929528941}{2000000}\right), \frac{28832688827}{125000}\right), y\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right)}, y\right), c\right), y\right), i\right)\right) \]

   5. Simplified 82.9%

      \[\leadsto \frac{\left(\color{blue}{y \cdot 27464.7644705} + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 7.8000000000000002e40 < y < 4.79999999999999984e166

   1. Initial program 3.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right)\right) \]

   4. Applied egg-rr 3.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}}} \]

   5. Taylor expanded in y around -inf

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y} + \frac{1}{x}\right)}\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{x} + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(\frac{1}{x}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \left(\color{blue}{-1} \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right), y\right)\right)\right)\right) \]

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{a}{x}\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right)\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left({x}^{2}\right)\right)\right)\right), y\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left(x \cdot x\right)\right)\right)\right), y\right)\right)\right)\right) \]

      13. *-lowering-*.f64 67.5%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right)\right)\right)\right) \]

   7. Simplified 67.5%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + \left(-\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{y}\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+32}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+40}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot 27464.7644705\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+166}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+164}:\\ \;\;\;\;\frac{-1}{\frac{-1}{x} + \left(\frac{z}{y \cdot \left(x \cdot x\right)} - \frac{\frac{a}{x}}{y}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -5.8e+33)
     t_1
     (if (<= y 2.35e+28)
       (/ t (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))
       (if (<= y 8.5e+164)
         (/ -1.0 (+ (/ -1.0 x) (- (/ z (* y (* x x))) (/ (/ a x) y))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -5.8e+33) {
		tmp = t_1;
	} else if (y <= 2.35e+28) {
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else if (y <= 8.5e+164) {
		tmp = -1.0 / ((-1.0 / x) + ((z / (y * (x * x))) - ((a / x) / y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-5.8d+33)) then
        tmp = t_1
    else if (y <= 2.35d+28) then
        tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    else if (y <= 8.5d+164) then
        tmp = (-1.0d0) / (((-1.0d0) / x) + ((z / (y * (x * x))) - ((a / x) / y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -5.8e+33) {
		tmp = t_1;
	} else if (y <= 2.35e+28) {
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else if (y <= 8.5e+164) {
		tmp = -1.0 / ((-1.0 / x) + ((z / (y * (x * x))) - ((a / x) / y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -5.8e+33:
		tmp = t_1
	elif y <= 2.35e+28:
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	elif y <= 8.5e+164:
		tmp = -1.0 / ((-1.0 / x) + ((z / (y * (x * x))) - ((a / x) / y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -5.8e+33)
		tmp = t_1;
	elseif (y <= 2.35e+28)
		tmp = Float64(t / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	elseif (y <= 8.5e+164)
		tmp = Float64(-1.0 / Float64(Float64(-1.0 / x) + Float64(Float64(z / Float64(y * Float64(x * x))) - Float64(Float64(a / x) / y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -5.8e+33)
		tmp = t_1;
	elseif (y <= 2.35e+28)
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	elseif (y <= 8.5e+164)
		tmp = -1.0 / ((-1.0 / x) + ((z / (y * (x * x))) - ((a / x) / y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+33], t$95$1, If[LessEqual[y, 2.35e+28], N[(t / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+164], N[(-1.0 / N[(N[(-1.0 / x), $MachinePrecision] + N[(N[(z / N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a / x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.80000000000000049e33 or 8.50000000000000027e164 < y

   1. Initial program 5.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)}{y}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)}{y}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), y\right)\right) \]

      9. *-lowering-*.f64 78.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   5. Simplified 78.1%

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]

   if -5.80000000000000049e33 < y < 2.34999999999999983e28

   1. Initial program 95.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{t}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 67.5%

      \[\leadsto \frac{\color{blue}{t}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 2.34999999999999983e28 < y < 8.50000000000000027e164

   1. Initial program 8.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right)\right) \]

   4. Applied egg-rr 8.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}}} \]
   5. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\left(\left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}\right) \cdot y\right), t\right)\right)\right) \]

      2. remove-double-div N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\left(\frac{1}{\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}}} \cdot y\right), t\right)\right)\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\left(\frac{1 \cdot y}{\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}}}\right), t\right)\right)\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\left(\frac{1}{\frac{\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}}}{1 \cdot y}}\right), t\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}}}{1 \cdot y}\right)\right), t\right)\right)\right) \]

      6. *-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}}}{y}\right)\right), t\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(y, a\right)\right), b\right)\right), c\right)\right), i\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\frac{1}{y \cdot \left(y \cdot \left(x \cdot y + z\right) + \frac{54929528941}{2000000}\right) + \frac{28832688827}{125000}}\right), y\right)\right), t\right)\right)\right) \]

   6. Applied egg-rr 8.6%

      \[\leadsto \frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{\color{blue}{\frac{1}{\frac{\frac{1}{y \cdot \left(y \cdot \left(z + y \cdot x\right) + 27464.7644705\right) + 230661.510616}}{y}}} + t}} \]

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\left(\frac{1}{x} + \frac{a}{x \cdot y}\right) - \frac{z}{{x}^{2} \cdot y}\right)}\right) \]
   8. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{x} + \color{blue}{\left(\frac{a}{x \cdot y} - \frac{z}{{x}^{2} \cdot y}\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(\frac{1}{x}\right), \color{blue}{\left(\frac{a}{x \cdot y} - \frac{z}{{x}^{2} \cdot y}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \left(\color{blue}{\frac{a}{x \cdot y}} - \frac{z}{{x}^{2} \cdot y}\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{\_.f64}\left(\left(\frac{a}{x \cdot y}\right), \color{blue}{\left(\frac{z}{{x}^{2} \cdot y}\right)}\right)\right)\right) \]

      5. associate-/r* N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{\_.f64}\left(\left(\frac{\frac{a}{x}}{y}\right), \left(\frac{\color{blue}{z}}{{x}^{2} \cdot y}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\frac{a}{x}\right), y\right), \left(\frac{\color{blue}{z}}{{x}^{2} \cdot y}\right)\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(a, x\right), y\right), \left(\frac{z}{{x}^{2} \cdot y}\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(a, x\right), y\right), \mathsf{/.f64}\left(z, \color{blue}{\left({x}^{2} \cdot y\right)}\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(a, x\right), y\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(\left({x}^{2}\right), \color{blue}{y}\right)\right)\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(a, x\right), y\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(\left(x \cdot x\right), y\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 62.9%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(a, x\right), y\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, x\right), y\right)\right)\right)\right)\right) \]

   9. Simplified 62.9%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + \left(\frac{\frac{a}{x}}{y} - \frac{z}{\left(x \cdot x\right) \cdot y}\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+33}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+164}:\\ \;\;\;\;\frac{-1}{\frac{-1}{x} + \left(\frac{z}{y \cdot \left(x \cdot x\right)} - \frac{\frac{a}{x}}{y}\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+40}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+167}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -1.7e+33)
     t_1
     (if (<= y 1.06e+40)
       (/
        (+ t (* y 230661.510616))
        (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))
       (if (<= y 1.8e+167)
         (/ -1.0 (+ (/ (- (/ z (* x x)) (/ a x)) y) (/ -1.0 x)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.7e+33) {
		tmp = t_1;
	} else if (y <= 1.06e+40) {
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else if (y <= 1.8e+167) {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-1.7d+33)) then
        tmp = t_1
    else if (y <= 1.06d+40) then
        tmp = (t + (y * 230661.510616d0)) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    else if (y <= 1.8d+167) then
        tmp = (-1.0d0) / ((((z / (x * x)) - (a / x)) / y) + ((-1.0d0) / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.7e+33) {
		tmp = t_1;
	} else if (y <= 1.06e+40) {
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else if (y <= 1.8e+167) {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -1.7e+33:
		tmp = t_1
	elif y <= 1.06e+40:
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	elif y <= 1.8e+167:
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -1.7e+33)
		tmp = t_1;
	elseif (y <= 1.06e+40)
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	elseif (y <= 1.8e+167)
		tmp = Float64(-1.0 / Float64(Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y) + Float64(-1.0 / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -1.7e+33)
		tmp = t_1;
	elseif (y <= 1.06e+40)
		tmp = (t + (y * 230661.510616)) / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	elseif (y <= 1.8e+167)
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+33], t$95$1, If[LessEqual[y, 1.06e+40], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+167], N[(-1.0 / N[(N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e33 or 1.80000000000000012e167 < y

   1. Initial program 5.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)}{y}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)}{y}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), y\right)\right) \]

      9. *-lowering-*.f64 78.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   5. Simplified 78.1%

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]

   if -1.7e33 < y < 1.05999999999999996e40

   1. Initial program 94.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{28832688827}{125000} \cdot y\right)}, t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right)}, y\right), i\right)\right) \]

      2. *-lowering-*.f64 81.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{28832688827}{125000}\right), t\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right)}, y\right), i\right)\right) \]

   5. Simplified 81.6%

      \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 1.05999999999999996e40 < y < 1.80000000000000012e167

   1. Initial program 3.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right)\right) \]

   4. Applied egg-rr 3.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}}} \]

   5. Taylor expanded in y around -inf

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y} + \frac{1}{x}\right)}\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{x} + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(\frac{1}{x}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \left(\color{blue}{-1} \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right), y\right)\right)\right)\right) \]

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{a}{x}\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right)\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left({x}^{2}\right)\right)\right)\right), y\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left(x \cdot x\right)\right)\right)\right), y\right)\right)\right)\right) \]

      13. *-lowering-*.f64 67.5%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right)\right)\right)\right) \]

   7. Simplified 67.5%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + \left(-\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{y}\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+33}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+40}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+167}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+24}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+166}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -9.5e+29)
     t_1
     (if (<= y 1.18e+24)
       (/ t (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))
       (if (<= y 5.1e+166)
         (/ -1.0 (+ (/ (- (/ z (* x x)) (/ a x)) y) (/ -1.0 x)))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -9.5e+29) {
		tmp = t_1;
	} else if (y <= 1.18e+24) {
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else if (y <= 5.1e+166) {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-9.5d+29)) then
        tmp = t_1
    else if (y <= 1.18d+24) then
        tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    else if (y <= 5.1d+166) then
        tmp = (-1.0d0) / ((((z / (x * x)) - (a / x)) / y) + ((-1.0d0) / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -9.5e+29) {
		tmp = t_1;
	} else if (y <= 1.18e+24) {
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else if (y <= 5.1e+166) {
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -9.5e+29:
		tmp = t_1
	elif y <= 1.18e+24:
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	elif y <= 5.1e+166:
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -9.5e+29)
		tmp = t_1;
	elseif (y <= 1.18e+24)
		tmp = Float64(t / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	elseif (y <= 5.1e+166)
		tmp = Float64(-1.0 / Float64(Float64(Float64(Float64(z / Float64(x * x)) - Float64(a / x)) / y) + Float64(-1.0 / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -9.5e+29)
		tmp = t_1;
	elseif (y <= 1.18e+24)
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	elseif (y <= 5.1e+166)
		tmp = -1.0 / ((((z / (x * x)) - (a / x)) / y) + (-1.0 / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+29], t$95$1, If[LessEqual[y, 1.18e+24], N[(t / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.1e+166], N[(-1.0 / N[(N[(N[(N[(z / N[(x * x), $MachinePrecision]), $MachinePrecision] - N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.5000000000000003e29 or 5.1e166 < y

   1. Initial program 5.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)}{y}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)}{y}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), y\right)\right) \]

      9. *-lowering-*.f64 78.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   5. Simplified 78.1%

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]

   if -9.5000000000000003e29 < y < 1.17999999999999997e24

   1. Initial program 95.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{t}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 67.5%

      \[\leadsto \frac{\color{blue}{t}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 1.17999999999999997e24 < y < 5.1e166

   1. Initial program 8.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right), \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t\right)}\right)\right) \]

   4. Applied egg-rr 8.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}}} \]

   5. Taylor expanded in y around -inf

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y} + \frac{1}{x}\right)}\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{x} + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(\frac{1}{x}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \left(\color{blue}{-1} \cdot \frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right)\right) \]

      5. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\left(\frac{-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}}{y}\right)\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \frac{a}{x} - -1 \cdot \frac{z}{{x}^{2}}\right), y\right)\right)\right)\right) \]

      7. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\left(-1 \cdot \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \left(\frac{a}{x} - \frac{z}{{x}^{2}}\right)\right), y\right)\right)\right)\right) \]

      9. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\left(\frac{a}{x}\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right)\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \left(\frac{z}{{x}^{2}}\right)\right)\right), y\right)\right)\right)\right) \]

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left({x}^{2}\right)\right)\right)\right), y\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \left(x \cdot x\right)\right)\right)\right), y\right)\right)\right)\right) \]

      13. *-lowering-*.f64 62.9%

          \[\leadsto \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{/.f64}\left(1, x\right), \mathsf{neg.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(-1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(a, x\right), \mathsf{/.f64}\left(z, \mathsf{*.f64}\left(x, x\right)\right)\right)\right), y\right)\right)\right)\right) \]

   7. Simplified 62.9%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + \left(-\frac{-1 \cdot \left(\frac{a}{x} - \frac{z}{x \cdot x}\right)}{y}\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+29}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+24}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+166}:\\ \;\;\;\;\frac{-1}{\frac{\frac{z}{x \cdot x} - \frac{a}{x}}{y} + \frac{-1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+37}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -1.25e+33)
     t_1
     (if (<= y 5.6e+37)
       (/ t (+ (* y (+ c (* y (+ b (* y (+ y a)))))) i))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.25e+33) {
		tmp = t_1;
	} else if (y <= 5.6e+37) {
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-1.25d+33)) then
        tmp = t_1
    else if (y <= 5.6d+37) then
        tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.25e+33) {
		tmp = t_1;
	} else if (y <= 5.6e+37) {
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -1.25e+33:
		tmp = t_1
	elif y <= 5.6e+37:
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -1.25e+33)
		tmp = t_1;
	elseif (y <= 5.6e+37)
		tmp = Float64(t / Float64(Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(y + a)))))) + i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -1.25e+33)
		tmp = t_1;
	elseif (y <= 5.6e+37)
		tmp = t / ((y * (c + (y * (b + (y * (y + a)))))) + i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+33], t$95$1, If[LessEqual[y, 5.6e+37], N[(t / N[(N[(y * N[(c + N[(y * N[(b + N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.24999999999999993e33 or 5.5999999999999996e37 < y

   1. Initial program 5.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)}{y}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)}{y}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), y\right)\right) \]

      9. *-lowering-*.f64 66.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   5. Simplified 66.4%

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]

   if -1.24999999999999993e33 < y < 5.5999999999999996e37

   1. Initial program 94.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{t}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 66.6%

      \[\leadsto \frac{\color{blue}{t}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+33}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+37}:\\ \;\;\;\;\frac{t}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) + i}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{if}\;y \leq -1.36 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+37}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (- (+ x (/ z y)) (/ (* x a) y))))
   (if (<= y -1.36e+26) t_1 (if (<= y 8.5e+37) (/ t (+ i (* y c))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.36e+26) {
		tmp = t_1;
	} else if (y <= 8.5e+37) {
		tmp = t / (i + (y * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z / y)) - ((x * a) / y)
    if (y <= (-1.36d+26)) then
        tmp = t_1
    else if (y <= 8.5d+37) then
        tmp = t / (i + (y * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (x + (z / y)) - ((x * a) / y);
	double tmp;
	if (y <= -1.36e+26) {
		tmp = t_1;
	} else if (y <= 8.5e+37) {
		tmp = t / (i + (y * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (x + (z / y)) - ((x * a) / y)
	tmp = 0
	if y <= -1.36e+26:
		tmp = t_1
	elif y <= 8.5e+37:
		tmp = t / (i + (y * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(x + Float64(z / y)) - Float64(Float64(x * a) / y))
	tmp = 0.0
	if (y <= -1.36e+26)
		tmp = t_1;
	elseif (y <= 8.5e+37)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (x + (z / y)) - ((x * a) / y);
	tmp = 0.0;
	if (y <= -1.36e+26)
		tmp = t_1;
	elseif (y <= 8.5e+37)
		tmp = t / (i + (y * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.36e+26], t$95$1, If[LessEqual[y, 8.5e+37], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35999999999999993e26 or 8.4999999999999999e37 < y

   1. Initial program 5.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(x + \frac{z}{y}\right), \color{blue}{\left(\frac{a \cdot x}{y}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{z}{y}\right)\right), \left(\frac{\color{blue}{a \cdot x}}{y}\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{a \cdot \color{blue}{x}}{y}\right)\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)}{y}\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \left(\frac{\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)}{y}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(-1 \cdot \left(a \cdot x\right)\right)\right), \color{blue}{y}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(a \cdot x\right)\right)\right)\right), y\right)\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\left(a \cdot x\right), y\right)\right) \]

      9. *-lowering-*.f64 66.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(x, \mathsf{/.f64}\left(z, y\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, x\right), y\right)\right) \]

   5. Simplified 66.4%

      \[\leadsto \color{blue}{\left(x + \frac{z}{y}\right) - \frac{a \cdot x}{y}} \]

   if -1.35999999999999993e26 < y < 8.4999999999999999e37

   1. Initial program 94.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{t}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 66.6%

      \[\leadsto \frac{\color{blue}{t}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(t, \mathsf{+.f64}\left(\color{blue}{\left(c \cdot y\right)}, i\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 58.9%

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(c, y\right), i\right)\right) \]

   8. Simplified 58.9%

      \[\leadsto \frac{t}{\color{blue}{c \cdot y} + i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+26}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+37}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{z}{y}\right) - \frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.5e+31) x (if (<= y 7.5e+32) (/ t (+ i (* y c))) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.5e+31) {
		tmp = x;
	} else if (y <= 7.5e+32) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-3.5d+31)) then
        tmp = x
    else if (y <= 7.5d+32) then
        tmp = t / (i + (y * c))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.5e+31) {
		tmp = x;
	} else if (y <= 7.5e+32) {
		tmp = t / (i + (y * c));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.5e+31:
		tmp = x
	elif y <= 7.5e+32:
		tmp = t / (i + (y * c))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.5e+31)
		tmp = x;
	elseif (y <= 7.5e+32)
		tmp = Float64(t / Float64(i + Float64(y * c)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -3.5e+31)
		tmp = x;
	elseif (y <= 7.5e+32)
		tmp = t / (i + (y * c));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.5e+31], x, If[LessEqual[y, 7.5e+32], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5e31 or 7.49999999999999959e32 < y

   1. Initial program 5.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 53.8%

      \[\leadsto \color{blue}{x} \]

   if -3.5e31 < y < 7.49999999999999959e32

   1. Initial program 95.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{t}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(y, a\right), y\right), b\right), y\right), c\right), y\right), i\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 67.0%

      \[\leadsto \frac{\color{blue}{t}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(t, \mathsf{+.f64}\left(\color{blue}{\left(c \cdot y\right)}, i\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 59.3%

         \[\leadsto \mathsf{/.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(c, y\right), i\right)\right) \]

   8. Simplified 59.3%

      \[\leadsto \frac{t}{\color{blue}{c \cdot y} + i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 49.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-34}:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.1e+30) x (if (<= y 1.4e-34) (/ t i) x)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.1e+30) {
		tmp = x;
	} else if (y <= 1.4e-34) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-1.1d+30)) then
        tmp = x
    else if (y <= 1.4d-34) then
        tmp = t / i
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.1e+30) {
		tmp = x;
	} else if (y <= 1.4e-34) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -1.1e+30:
		tmp = x
	elif y <= 1.4e-34:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.1e+30)
		tmp = x;
	elseif (y <= 1.4e-34)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -1.1e+30)
		tmp = x;
	elseif (y <= 1.4e-34)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.1e+30], x, If[LessEqual[y, 1.4e-34], N[(t / i), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e30 or 1.39999999999999998e-34 < y

   1. Initial program 13.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 48.6%

      \[\leadsto \color{blue}{x} \]

   if -1.1e30 < y < 1.39999999999999998e-34

   1. Initial program 97.3%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{t}{i}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 51.3%

         \[\leadsto \mathsf{/.f64}\left(t, \color{blue}{i}\right) \]

   5. Simplified 51.3%

      \[\leadsto \color{blue}{\frac{t}{i}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 25.3% accurate, 33.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return x;
}

Python

def code(x, y, z, t, a, b, c, i):
	return x

Julia

function code(x, y, z, t, a, b, c, i)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := x

Derivation

1. Initial program 53.3%

   \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 26.9%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024138 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))